Integers and the Number Line

The integers are the whole numbers together with their negatives and zero:

We picture them on a number line. Zero sits in the middle, positive numbers stretch to the right, negative numbers to the left. A number to the right is always greater; a number to the left is always smaller.

That single rule settles every comparison. For example $-5 < -2$, because $-5$ lies further left. Do not be fooled by the digits: $5$ is bigger than $2$, but $-5$ is smaller than $-2$.

Worked example. Order from coldest to warmest: $-3, 2, -7, 0, 5$. Reading the number line left to right gives $-7, -3, 0, 2, 5$.

Exam checkpoint

In a test, turn each story into a position relative to zero before you compare it. Temperature below freezing, a debt and a basement level are negatives; money in credit, altitude above sea level and a positive score are positives. Say the comparison aloud: ‘-9 is left of -2, so -9 is smaller.’ This stops the common mistake of comparing only the digits.

Short worked example. A lift begins at floor 0, goes down to B4 and then up to floor 2. The locations are $-4$ and $2$. Since $-4$ is left of $2$, the basement is lower.